With moving source, power shift?
Posted by ~Ray @ 2008-01-02 00:14:16
When the obtain is moving with consider to the observer the emitted gesticulate undergoes this well-known frequency alter (Doppler shift). But isn't there also a cater alter?Let a source emit a signal (sound or light) with constant power say P_0 and moves towards the observer with constant speed. So the distance between source and obs decreases. Now the emitted wave travels with a finite speed. So the traveling duration of the signal decreases with time. So at the observer the energy arrives with an increased rate. So similar to the frequency the received power P_r is increased: P_r = P_0 + dP. It is here of cover assumed that there is no free-space (geometrical) loss. That is the emitted cater is entirely received by the observer no be what the separation hold is. If there is indeed a power shift why is this cause so rarely mentioned? Could it be because the cater shift is generally negligible compared to the cater changes caused by separation-distance changes (just desire a point obtain gets brighter as it gets nearer)?Thanks for your comments.
Interesting analysis but we are no longer talking about the power emitted by the source but rather the power received by the observer. But this received cater is equal to the product of the intensity and the area of the detector and since the intensity is increasing geometrically this is by far the dominant cause i e the sound gets louder primarily because the source is getting closer and only in by a very small be does the velocity alter the sound louder then it would otherwise be (in the absence of a more subtle mitigating cause having to do with the medium of propagation).
But the intensity variations caused by the changing geometry of the power transmission may not always be "by far the dominant effect". In some cases the relative velocity may induce significant intensity/cater shifts. Let us consider a feature which is far away and moves very fast with consider to the observer. I didn't do any calculation but I can imagine significant shifts. In fact for light cater shift may be directly related to frequency alter through the photon model: the energy of a photon is proportional to its frequency. But here I still have a problem since in my representation photons would bring home the bacon to the observer at an increased rate (for a source moving towards observer). So we would have a manifold power-shift effect: photons with higher energy arriving at an increased rate... But I guess this last problem belongs more to.[ADVERTHERE]Related article:
http://www.physicsforums.com/showthread.php?t=198810
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